A quantitative understanding of bonding in condensed matter systems demands a solution of the many electron problem. This course will show how the many electron problem can be mapped onto single electron problems in an approximate way using the Hartree and Hartree Fock approximations and a formally exact way using (density functional theory and the Kohn Sham equations. Further, some of the methodology used to solve the Kohn Sham equations in complex systems will be described. In the last part of the lectures, some extensions and examples will be analysed, and we will critically evaluate the strength and weaknesses of DFT and other ab-initio electronic structure methods.
Niels is a professor of theoretical physics at the University of Manchester. His research interests are in the theory of condensed matter and nuclear physics, combining computational and theoretical approaches, using many-body and ab initio techniques. He has a special interest in twistronics and higher-order topological materials. Outside physics, he works as associate Dean for Teaching and Learning in the Faculty of Science and Engineering.
Statistical Mechanics aims to provide a macroscopic description of a physical system starting from knowledge of its microscopic properties. The methodology and techniques are widely used throughout condensed matter physics and are also today being applied to understand the dynamics of model ecologies, economies and societies. In these lectures, we will revisit the equilibrium properties of matter – such as phase transitions and universality – from the perspective of dynamics (as opposed to statics, as is typically done in undergraduate courses). Then we will examine successively further-from-equilibrium systems, ending with a discussion of fluctuations in driven systems, a subject currently generating considerable excitement in this field.
Richard Blythe is a Professor of Complex Systems at the University of Edinburgh. Since his PhD days, he has been researching models and theories for nonequilibrium dynamical systems. Applications of these models include transport in biological systems, traffic flow, population dynamics and language change.
This course deals mainly with the influence of interactions on the electrons in materials. We begin with a review of second quantisation and the Fermi gas theory of metals, and then progress to Landau’s Fermi liquid theory and the notion of quasiparticles. The effect of impurities on the Fermi liquid (including the Kondo effect) is discussed, and we then move on to consider how the Fermi liquid gives way to other phases as the interactions are increased, concentrating on the Stoner instability and the Mott insulator. We analyse the magnetism in the Mott insulating phase, developing the concept of spin waves. Finally, we make a survey of some experimental data on strongly correlated crystalline solids, giving basic interpretations in terms of the concepts developed in the course.
Chris is a reader at the University of St Andrews. He works on various topics in the theory of strong correlations, including non-Fermi-liquids, highly frustrated magnets, non-equilibrium atomic fluids, and vortex-mediated phase transitions.
Quantum fluids are those many-particle systems in whose behaviour the effects of both the quantum mechanics and quantum statistics are important. They range from atoms and molecules, such as liquid Helium 4He and 3He and dilute atomic alkali gases, photons interacting via coupling to some matter component to electrons in metals and other solid state quasiparticles such as excitons, polaritons and magnons. In these lectures we explore collective properties of such systems. We begin by discussing the principal quantum collective phenomenon, which lies at the heart of many related concepts, that of a Bose-Einstein condensation in bosonic systems. We then progress to look at how fermions can cooperate to also “bose-condense” and how it is possible to cross from “fermionic” to “bosonic” condensates by changing particle density and/or interaction strength – the BCS-BEC crossover. We then discuss one of the most exciting manifestations of many particle quantum collective behaviour that of superfluidity. We also review physical experimental systems focusing on ultra-cold atomic gases, excitons and polaritons, and interacting photons in various settings. We closes the course with a short discussion of strongly interacting quantum systems such as atoms in optical lattices and coupled cavity lattices.
Marzena is Professor of Physics at University College London
This course will give you a practical guide to density functional theory (DFT), including running a series of simulations to model and study quantum phase transition in a crystalline system. Upon completing this course, you should be able to set up a DFT calculation, interpret the output results and post-process them using complementary techniques such as Wannier interpolation.
Saeed is a lecturer in theoretical physics at the University of Manchester. His research is focused on first-principles modelling of topological quantum phase transition, superconductivity and quasiparticle dynamics of strongly correlated electrons in low-dimensional crystalline systems.
Mesoscopic physics is the name given to electronic behaviour in solid state nanostructures that are so small that their size is similar to relevant characteristic length scales. Examples of such length scales include the elastic mean free path (which governs the scale for ballistic transport), the phase coherence length (quantum interference effects), and the electronic wavelength (quantum confinement). The aim of this course is to describe key experimental transport phenomena including weak localisation, universal conductance fluctuations, Aharonov-Bohm oscillations, and conductance quantisation whilst giving an overview of theoretical methods such as the tight binding model, the Landauer-Büttiker formulism, scattering theory, and scaling theory.
Ed McCann works in the condensed matter theory group at Lancaster University. Recently, his research has been focussed on the properties of chiral electrons in graphene and graphene multilayers, looking at their transport and spectroscopic properties.
This lecture series will introduce the use of quantum information techniques for the study of correlated problems in quantum matter. First, the general notion of quantum information and entanglement will be introduced, alongside the notions of matrix product states and tensor networks. The lectures will then go on to give examples of these in topical problems such as dynamics, thermalisation, and many-body localisation.
Zlatko is an Associate Professor in Theoretical Physics at University of Leeds. He obtained his PhD at Université Paris Sud in 2010. He was a postdoctoral researcher at Princeton University (2010-2013), and a joint postdoctoral fellow between Perimeter Institute and Institute for Quantum Computing in Waterloo (2013-2015). His research spans condensed matter theory and quantum information, focusing on topology and dynamics in quantum many-body systems, such as topological phases of matter, the fractional quantum Hall effect, and many-body localisation.
The well-known Landau theory of phase transitions classifies phases of matter according to broken symmetries and local order parameters, such as solids that break translational symmetry, or magnets that break magnetic rotation symmetry. It has been long known that there are phases of matter that defy this classification — the quantum Hall state being the most obvious (but by no means only) example. With the discovery of topological insulators about 10 years ago, interest in this field has exploded, and we now know of many distinct phases of matter with no local order parameter, but instead characterised by a topological invariant. This short lecture course will focus mostly on non-interacting band theory, and introduce topological invariants, boundary states, and the bulk-boundary correspondence necessary to understand the modern topic of topological insulators. Other manifestations of topology in modern condensed matter physics will also be exposed, although not discussed in detail.
Sam works on the theory of strongly correlated systems, specialising in low-dimensional systems both in and out of equilibrium. He has worked in groups in the US, Italy and Germany, and since 2013 has been a lecturer at the University of Kent in Canterbury.